1.
It is normal for a motor to draw surge current when started up, while it comes up to speed. This might take a second or two.
However perhaps for an A/C it takes a minute before it reaches its most efficient operating state.
2.
Common advice says you should wait a few minutes after turning off an A/C, before you turn it on again.
The reason is because liquid refrigerant remains in the compressor when you shut it off. Since it is impossible to compress the liquid, therefore the compressor pump cannot turn.
You should cut off power immediately because a stalled motor draws extreme current.
After a few minutes, the liquid turns to gas. Then the pump will turn when powered up.
If you leave power connected to a stalled motor for a long enough time, it could change the operating characteristics of the motor.